# What is the axis of symmetry and vertex for the graph 2(y - 2) = (x + 3)^2?

Nov 21, 2016

The vertex is at $\left(- 3 , 2\right)$ and the axis of symmetry is $x = - 3$

#### Explanation:

Given: $2 \left(y - 2\right) = {\left(x + 3\right)}^{2}$

The vertex form for the equation of a parabola is:

$y = a {\left(x - h\right)}^{2} + k$

where "a" is coefficient of the ${x}^{2}$ term and $\left(h , k\right)$ is the vertex.

Write the (x + 3) in the given equation as (x - -3):

$2 \left(y - 2\right) = {\left(x - - 3\right)}^{2}$

Divide both sides by 2:

$y - 2 = \frac{1}{2} {\left(x - - 3\right)}^{2}$

Add 2 to both sides:

$y = \frac{1}{2} {\left(x - - 3\right)}^{2} + 2$

The vertex is at $\left(- 3 , 2\right)$ and the axis of symmetry is $x = - 3$